Power transmission

ABSTRACT

A power servo system which includes an actuator coupled to a load and receives an input command signal indicative of desired motion at the load. A sampled-data control system receives and samples input signals indicative of desired and actual motion at the hydraulic actuator and load, and provides control signals to the actuator necessary to obtain desired motion. The sampled-data control system includes digital processing circuitry with series and feedback compensation, coordinated with the hydraulic system transfer function, to form a complete closed-loop control system operating in the sampled-data or Z-transform domain. Different equation constants in the series and feedback compensation circuitry are recalculated periodically. In one embodiment of the invention, such constants are recalculated as a function of system behavior, so that system control automatically varies with operating conditions. In another embodiment of the invention, system constants are calculated based upon a single operator-variable (or remote system) input, which accommodates rapid operator-implemented tracking of system behavior while reducing calculation time.

The present invention relates to power transmissions, and moreparticularly to power servo control systems, e.g. electric,electropneumatic and/or electrohydraulic servo control systems.

BACKGROUND OF THE INVENTION

It is conventional practice in the art of electrohydraulic servo controlsystems to provide a command signal indicative of position, velocity,acceleration or pressure desired at the controlled mechanism, to measureactual position, velocity and acceleration at the controlled mechanismby means of corresponding transducers, and to drive a hydraulic actuatorwith an error signal representative of a difference between the commandsignal and the measured motion variables. Provision of three transducersmounted on or otherwise responsive to the controlled mechanism increasessignificantly the overall expense of the servo system while at the sametime reducing overall reliability. The aforementioned deficiencies areparticularly acute in the field of industrial robotics where interest incost, simplicity and reliability is continually increasing.

U.S. patent application Ser. No. 418,086, filed Sept. 14, 1982 andassigned to the assignee hereof, now U.S. Pat. No. 4,502,109, disclosesan electrohydraulic servo control system having three dynamic statevariables, namely position, velocity and acceleration. A control systemincludes a sensor coupled to the hydraulic actuator for measuring loadposition, and a digital observer responsive to measured position forestimating velocity and acceleration. Signals indicative of measuredand/or estimated state variables are compared with an input statecommand signal to obtain a difference of error signal which drives theactuator. The observer electronics includes a digital microprocessorsuitably programmed to estimate the state variables as solutions tocorresponding linear equations. The several equation constants, whichare functions of actuator and driven mass characteristics, are enteredthrough a corresponding multiplicity of operator-adjustable resistors.U.S. patent application Ser. No. 699,039, filed Feb. 7, 1985, now U.S.Pat. No. 4,581,699, as a continuation-in-part of Ser. No. 418,086, andlikewise assigned to the assignee hereof, discloses a modification tothe parent disclosure wherein the several equation constants aredown-loaded from a remote system into observer storage registers.

Although the technology disclosed in the above-referenced patentapplications presents a significant step forward in the art, improvementremains desirable in a number of areas. For example, the need tocalculate the several state variables as solutions to a correspondingnumber of equations at each input sampling interval is quite timeconsuming, placing limitations on speed of operation and the number oftasks that can be performed. Furthermore, the requirement that systemconstants be loaded into the observer system limits adaptability of thesystem for changing conditions, such as wear or hydraulic fluid pressurevariation.

OBJECTS AND SUMMARY OF THE INVENTION

A general object of the present invention, therefore, is to provide aservo control system which is self-adaptive in operation, i.e. whichperiodically updates some or all system constants to accommodatechanging conditions, and which is configured to obtain improved speed ofcalculation.

Another object of the invention is to provide a servo control systemwhich obtains the foregoing objectives, and yet remains economical andreliable to implement.

The present application discloses sampled-data feedback control systemswherein control is obtained by sampling the various control and errorsignals at discrete periodic intervals. Sampled-data control systems ofthis character are to be distinguished from continuous analog controlsystems. For purposes of disclosure and description, it is convenient toconsider construction and operation of the sampled-data feedback controlsystems of the invention in the so-called sampled-data or Z-transformdomain. In systems of the subject type, which may be described by lineardifference equations with constants that do not vary significantlybetween sample intervals, Z transformation of system transfer functionsyields rational polynomial ratios in the variable "Z". This variable iscomplex and is related to the more-recognized Laplace transform variable"S" by the equation

    Z=e.sup.TS                                                 ( 1)

where T is sampling interval. Indeed, in Z-transform theory, suchconcepts as transfer functions, mapping theorems, combinatorial theoremsand inversions are related to sampled-data systems in a manner in manyways comparable to the relationship of the Laplace transformation tocontinuous systems. A more complete discussion of sampled-data controlsystems and Z-transform theory is provided in Ragazzini and Franklin,Sampled-Data Control Systems, Mc-Graw-Hill (1958).

In accordance with the embodiments of the invention herein disclosed, asampled-data control system receives and samples input signalsindicative of desired and actual motion at a hydraulic actuator andload, and provides control signals to the actuator necessary to obtaindesired motion. The sampled-data control system includes digitalprocessing circuitry with series and feedback compensation, coordinatedwith hydraulic system behavior function, to form a complete closed-loopcontrol system operating in the sampled-data or Z-transform domain.Difference equation constants in the series and feedback compensationcircuitry are recalculated at each sampling interval. In one embodimentof the invention, such constants are recalculated as a function ofsystem behavior, so that system control automatically varies withoperating conditions or load. In another embodiment of the invention,system constants are calculated based upon a single operator-variable(or remote system) input, which accommodates rapid operator-implementedtracking of system behavior while reducing calculation time.

BRIEF DESCRIPTION OF THE DRAWINGS

The invention, together with additional objects, features and advantagesthereof, will be best understood from the following description, theappended claims and the accompanying drawings in which:

FIG. 1 is a functional block diagram of a basic electrohydraulic servocontrol system in accordance with the prior art;

FIG. 2 is a functional block diagram of a basic hydraulic control systemin accordance with the present invention;

FIG. 3 is a more detailed functional block diagram of the sampled-datadigital controller in FIG. 2 in accordance with one embodiment of theinvention;

FIG. 4 is a detailed functional block diagram of the sampled-datadigital controller of FIG. 2 in accordance with a second embodiment ofthe invention;

FIG. 5 is a fragmentary block diagram illustrating a further embodimentof the invention;

FIG. 6 is a graphic illustration of operation of a further embodiment ofthe invention; and

FIG. 7 is an electrical schematic drawing of an electronic controller inaccordance with a presently preferred embodiment of the invention.

FIG. 1 illustrates a conventional position command electrohydraulicservo control system 10 as comprising a valve actuator system or plant12, which includes an electrohydraulic valve coupled by an actuator to aload. The actuator system, including the load, is characterized by aninertial mass and spring elasticity. A position sensor or transducer 14is suitably mechanically coupled to the actuator and load to provide anelectrical output signal Y as a function of actual actuator and loadposition. A position command or reference signal R from an operatorjoystick 15, for example, is fed to a summer 16, which provides an errorsignal E as a function of the difference between the command signal Rand the actual position signal Y. The error signal E, fed through asuitable amplifier having gain 18, controls operation of actuator 12. Itwill be appreciated that summer 16 and gain 18 would typically becombined in a single amplifier. System 12 and transducer 14 may be ofany suitable types, and indeed may be contained within a singleassembly.

FIG. 2 illustrates an electrohydraulic servo control system 20 embodyinga sampled-data digital controller 22 in accordance with the presentinvention. Within controller 22, a first sample-and-hold circuit 24receives and samples command signal R from joystick 15, and provides acorresponding Z-transformed output signal R(Z) in the sampled-datadomain. A second sample-and-hold circuit 26 receives and samplesposition signal Y from sensor 14, and provides a correspondingZ-transformed output signal Y(Z) in the sampled-data domain. A feedbackcompensator 28 receives the output Y(Z) of circuit 26 and provides acompensation signal Q(Z) to one input of a summer 30. Summer 30 receivesa second input R(Z) from circuit 24, and provides a difference or errorsignal E(Z) to a series compensator 32. Compensator 32 provides acommand signal U(Z) through a zero-order-hold circuit 33 to plant 12.

For an electrohydraulic plant 12, including a hydraulic valve, actuatorand spring, it can be shown that the transfer function of plant 12 inthe sampled-data domain is: ##EQU1## where B₁, B₂, B₃, α₁, α₂ and α₃ areconstant functions of plant parameters and sampling time. Assuming zerodamping, expression (2) reduces to: ##EQU2## B₁, B₂ and α are given bythe equations: ##EQU3## where K₅ is a gain constant, T is samplingperiod and ω is neutral stability resonant frequency of plant 12. All ofthese constants are measurable or estimatable in accordance withpreferred aspects of the invention to be discussed. The transferfunction of system or plant 12 is thus predetermined as a function ofplant characteristics.

The orders of the Z-domain transfer functions of compensators 28, 32 areselected to obtain desired step response and computation time. In apreferred embodiment of the invention, the transfer function ofcompensator 28 is: ##EQU4## and the transfer function of compensator 32is: ##EQU5## where G₁, G₂, G₃, C₁, C₂ and C₃ are constants, and P(Z) isa polynomial in Z which, in the preferred embodiments of the inventionhereinafter discussed, is set equal to unity. First and second orderpolynomials for the transfer function of compensator 32 are alsocontemplated. Thus, in the general case, where the transfer function ofplant 12 is of order N in the Z-domain, with N being an integer greaterthan one, the transfer function of compensator 28 is of order N-1, andthe transfer function of compensator 32 is N or less (i.e., not greaterthan N).

For the overall system to be stable, including plant 12 and controller22, all poles must be within the Z-plane unit circle. Ragazzini andFranklin, supra et ch. 4. The overall closed-loop transfer function,embodying the individual functions of expressions (3), (7) and (8), is asixth order expression in Z. Thus, six poles are needed. Choosing allsix poles at location -a within the Z-plane unit circle means that##EQU6## Combining expressions (2), (6) and (7), and equatingcoefficients with corresponding coefficients in equation (8), yields:##EQU7## For a given value of pole location -a, and values of constantsB₁, B₂ and α per equations (4)-(6), equation (10) can be solved forconstants G₁, G₂, G₃, C₁, C₂, C₃.

FIG. 3 illustrates a modified controller 34 wherein the constants α, B₁and B₂ are continuously estimated and updated based upon systemperformance, and the internal transfer function constants C₁,C₂, C₃ andG₁,G₂,G₃ are likesise updated to obtain desired performance. In FIG. 3,an identifier 36 receives the Z-transformed position output Y(Z) ofcircuit 26 (FIG. 2) and the Z-domain command signal U(Z) fromcompensator 32. Identifier 32 estimates constants α,B₁ and B₂ as will bedescribed, and feeds such estimated constants to the circuit block 38wherein constants C₁,C₂,C₃ and G₁,G₂,G₃ are calculated per equation(10). The latter constants are then fed to associated compensators32,28.

Briefly stated, identifier 36 estimates constants α,B₁ and B₂periodically as a function of command signal U(Z) and system responseY(Z) thereto over a number of preceding intervals corresponding to theorder of the system. More specifically, at sample time (KT-2T), thediscrete equation of plant 12 is: ##EQU8## At time (KT-T), such equationis: ##EQU9## And at time (kT): ##EQU10## Equations (11)-(13) may becombined and rearranged as follows: ##EQU11## The values of Y(Z) andU(Z) are physically sampled and stored over the required number ofintervals, i.e. six for a third order plant, and constants, α, B₁ and B₂are estimated accordingly per equation (14).

Estimation of constants α, B₁ and B₂ per equation (14) has been found tobe more time-consuming than desirable for real-time controlapplications. It will be noted from equations (4)-(6) that B₁ and B₂ canbe determined from α based upon the common factor ω. In accordance witha modification to be discussed, identifier 36 (FIG. 3) first estimatesα, and then estimates B₁ and B₂ from α. However, such computation basedupon equations (4)-(6) involving trigometric functions would be too timeconsuming. Accordingly, equations (4)-(6) are first rewritten usingTaylor series expansion, and neglecting higher-order terms, as follows:##EQU12## Defining (ωT)² as Y, and solving equation (15) for Y yields

    Y=6±2(3α).sup.1/2                                 (18)

The positive sign yields a trivial solution and is ignored. The result:##EQU13## Thus, constant α is determined per equation (14), andconstants B₁ and B₂ are determined per equations (18)-(20). It has beenfound, somewhat surprisingly, using the specific embodiment of FIG. 7(to be described), that estimation of B₁ and B₂ per equations (18)-(20)is not only faster than solution of equation (14) for α, B₁ and B₂, butis also more accurate.

FIG. 4 illustrates a modification to FIG. 3 wherein a modifiedidentifier 40 receives a single input indicative of constant α from anadjustable resistor 42. Constants B₁,B₂ are calculated per equations(18)-(20). This modification is thus semi-automatic in that all systemconstants are derived from a single operator-adjustable input. It willbe appreciated that the α-indicating input to identifier 40 could alsobe fed from a remotely located control system or the like. Themodification of FIG. 4 has the advantage of eliminating the timeconsuming solution for from matrix equation (14).

The embodiment of FIG. 4 may be made semi-adaptive by means of themodification of FIG. 5 wherein the modified identifier 44 additionallyreceives an input U(Z) from compensator 32. In FIG. 6, graph 46illustrates position Y versus compensated command signal U (in the timedomain) for an optimally tuned system. It will be noted that commandsignal U, which is a function of error E, is substantially free ofoscillations. Graph 48 in FIG. 6 illustrates response of a system whichis not properly tuned, i.e. wherein α set by resistor 42 (FIG. 5) is notproperly set. Modified identifier 44 tunes the α input from resistor 42to provide a modified constant α', as well as constants B₁, B₂, tocalculator 38. This is accomplished in one embodiment of the inventionby counting peaks in the U input signal during a set-up operation andmodifying the α input to minimize such peaks. In another embodiment, thelength of the U signal curve is measured by time integration during thesetup operation, and the α input is internally modified to minimize suchlength. In all of these embodiments, modified identifier 44 isself-adaptive in set-up and continuous operation.

FIG. 7 is an electrical schematic drawing of a presently preferredembodiment of a microprocessor-based electronic controller, and acorresponding computer program in Intel 8051 machine language forimplementing the embodiments of FIGS. 4 and 5 (operator selectable) isappended to this specification. The R(Z),U(Z) and α inputs are connectedthrough multiplexer circuitry 50 to a serial input port of an Intel 8051microprocessor 52. Microprocessor 52, which possesses internal programmemory, is connected through a latch 54 and a decoder 56 to a pair of 4Kmemory modules 58,60. The output port of microprocesor 52 is connectedthrough an amplifier 62 to the valve actuator coil 64 of plant 12. Itwill be appreciated that identifier 40 (FIG. 4) or 44 (FIG. 5),compensators 28,32, constant calculator 38 and zero order hold circuit33 illustrated functionally in FIGS. 4 and 5 are all contained withinprogrammed microprocessor 52 and associated memory. ##SPC1##

The invention claimed is:
 1. A power servo system which includesactuator means adapted to variably actuate a load, said actuator meanshaving a predetermined first polynomial transfer function in thesampled-data domain having a plurality of first constants related todynamic behavior characteristics at said actuator means, andsampled-data servo control means including means for receiving a commandsignal, sensor means responsive to said actuator means for providing asensor signal as a function of actuation at said actuator means, andmeans for providing an error signal to control said actuator means as acombined function of said command signal and said sensor signal toobtain a preselected response characteristic at said actuator means,characterized in that said means for providing said error signalcomprisesmeans for periodically sampling said sensor signal to provide asampled sensor signal, feedback compensation means receiving saidsampled sensor signal and having a preselected second transfer functioncoordinated with said first transfer function to obtain said preselectedresponse characteristics, said second transfer function in thesampled-data domain being a polynomial having a number of secondconstants which vary at functions of said first constants, meansresponsive to said feedback compensation means and to said commandsignal to provide said error signal, means for providing a signalindicative of actuation at said actuator means, and means coupled tosaid feedback compensation means and responsive to said actuation signalover a number of sampling intervals for providing said second constantsas a continuing function of actuation at said actuator means.
 2. Thesystem set forth in claim 1 wherein said means coupled to said feedbackcompensation means includes first means responsive to said actuationsignal for estimating with first constants, and second means coupled tosaid first means for calculating said second constants as a function ofestimated first constants.
 3. The system set forth in claim 2 whereinsaid first means includes means for receiving said error signal and saidsampled sensor signal, and means for estimating said first constants asa combined function of said error and sampled sensor signals.
 4. Thesystem set forth in claim 2 wherein said first means includes means forreceiving an input signal indicative of one of said first constants, andmeans for estimating the remainder of said first constants as a combinedfunction of said actuator signal and said one of said first constants.5. The system set forth in claim 4 wherein said actuator signalcomprises said error signal.
 6. The system set forth in claim 2 furthercomprising series compensation means responsive to said error signal toprovide a drive signal to said actuator means, said series compensationmeans having a third transfer function which in the sampled-data domainis a polynomial having a number of third constants which vary asfunctions of said first constants, andthird means coupled to said firstmeans for calculating said second constants as a function of saidestimated first constants.
 7. The system set forth in claim 6 whereinsaid first transfer function is a polynomial of order N in thesampled-data domain, wherein said second transfer function is apolynomial of order N-1 in the sampled-data domain and said thirdtransfer function is a polynomial of order not greater than N in thesampled-data domain, with N being an integer greater than one.
 8. Apower servo system which includes actuator means adapted to variablyactuate a load, said actuator means having a predetermined firstpolynomial transfer function in the sampled data domain, sampled-dataservo control means including means for receiving an actuator commandsignal, sensor means responsive to said actuator means for providing asensor signal as a function of actuation at said actuator means, andmeans for providing an error signal to control said actuator means as acombined function of said command signal and said sensor signal toobtain a preselected response characteristic at said actuator means,characterized in that said means for providing said error signalcomprisesmeans for periodically sampling said sensor signal to provide asampled sensor signal, feedback compensation means receiving saidsampled sensor signal and having a preselected second transfer functioncoordinated with said first transfer function to obtain said preselectedresponse characteristic, said second transfer function being apolynomial in the sampled-data domain having a plurality of secondconstants which vary as a function of said first constants, meansresponsive to said feedback compensation means and to said commandsignal to provide said error signal, first means for receiving an inputsignal indicative of one of said first constants, second meansresponsive to said input signal for estimating the remainder of saidfirst constants, and third means coupled to said feedback compensationmeans and to said first and second means for calculating said secondconstants based upon said first constants.
 9. The system set forth inclaim 8 further comprising means for providing a signal indicative ofactuation at said actuator means, andwherein said second means comprisesmeans for estimating said remainder of said first constants as acombined function of said actuator signal and said one of said firstconstants.
 10. The system set forth in claim 9 wherein said first meansincludes means responsive to said input signal for estimating said oneof said first constants, and means responsive to said actuator signalfor revising said estimated one of said first constants as a function ofactuation at said actuator means.
 11. The system set forth in claim 8further comprising series compensation means responsive to said errorsignal to provide a drive signal to said actuator means, said seriescompensation means having a preselected third transfer function which inthe sampled-data domain is a polynomial coordinated with said first andsecond transfer functions to obtain said preselected responsecharacteristic and having a number of third constants which vary asfunctions of said first constants, andthird means coupled to said firstmeans for calculating said second constants as a function of said firstconstants.
 12. The system set forth in claim 11 wherein said firsttransfer function is a polynomial of order N in the sampled data domain,wherein said second transfer function is a polynomial or order N-1 inthe sampled-data domain and said third transfer function is a polynomialof order not greater than N in the sampled-data domain, with N being aninteger greater than one.
 13. A power servo system which includesactuator means adapted to variably actuate a load, said actuator meanshaving a predetermined first polynomial transfer function in thesampled-data domain having a plurality of first constants related todynamic behavior characteristics at said actuator means, andsampled-data servo control means including means for receiving a commandsignal, sensor means responsive to said actuator means for providing asensor signal as a function of actuation at said actuator means, andmeans for providing an error signal to control said actuator means as acombined function of said command signal and said sensor signal toobtain a preselected response characteristic at said actuator means,characterized in that said means for providing said error signalcomprisesmeans for periodically sampling said sensor signal to provide asampled sensor signal, feedback compensation means receiving saidsampled sensor signal and having a preselected second transfer functioncoordinated with said first transfer function to obtain said preselectedresponse characteristics, said second transfer function in thesampled-data domain being a polynomial having a number of secondconstants which vary as functions of said first constants, first meansfor estimating said first constants, second means responsive to saidfirst means and coupled to said feedback compensation means forcalculating said second constants as a function of estimated firstconstants, and means responsive to said feedback compensation means andto said command signals to provide said error signal.
 14. The system setforth in claim 13 further comprising series compensation meansresponsive to said error signal to provide a drive signal to saidactuator means, said series compensation means having a third transferfunction which in the sampled-data domain is a polynomial having anumber of third constants which vary as functions of said firstconstants, andthird means coupled to said first means for calculatingsaid third constants as a function of said estimated first constants.15. The system set forth in claim 14 wherein said first transferfunction is a polynomial of order N in the sampled-data domain, whereinsaid second transfer function is a polynomial of order N-1 in thesampled-data domain and said third transfer function is a polynomial oforder not greater than N in the sampled-data domain, with N being aninteger greater than one.
 16. The system set forth in claim 15 whereinsaid actuator means is an electrohydraulic actuator in which said firsttransfer function in the sampled-data domain is given by the expression:##EQU14## where B₁, B₂ and are constant functions of plant parametersgiven by the equations: ##EQU15## where K₅ is a gain constant, T issampling period, ω is neutral stability resonant frequency of saidactuator means, and Z is the sampled data domain transform variable. 17.The system set forth in claim 16 wherein said second transfer functionis given by the expression:

    G.sub.1 Z.sup.2 +G.sub.2 Z+G.sub.3

and wherein said third transfer function is given by the expression:##EQU16## where G₁,G₂,G₃,C₁,C₂,C₃ are constants related to saidconstants α, B₁ and B₂ by the expression: ##EQU17##
 18. The system setforth in claim 17 further comprising means for receiving an input signalindicative of said constant α, and means for estimating said constantsB₁,B₂ from said input signal according to the expression: ##EQU18##where Y=6+2(3α)^(1/2).